Analyzing interrupted time series with count outcomes using single or multiple control time series

Interrupted time series (ITS) analysis is a widely used quasi-experimental design for evaluating the impact of population-level interventions. To control for confounding from concurrent events, researchers often incorporate control time series. However, for count outcomes, especially with control series, methodological development remains limited.

We introduce a likelihood-based framework for controlled ITS analysis with count data. The proposed framework is based on a conditional Poisson likelihood and naturally extends to settings with multiple control series. This analysis is straightforward when the intervention and control series share a common time-varying component, whereas more flexible modeling is required when such shared structure is not supported. We describe a data-driven method for assessing whether the intervention and control series share a common time-varying component. We also show that, with robust variance estimation, the proposed approach can provide valid statistical inference even if the assumed distribution is misspecified.

We demonstrate the method using two real datasets. The first example assesses the effect of Florida's Stand Your Ground (SYG) law on firearm-related homicides and illustrates how the use of multiple control series (homicide rates in other states) leads to more accurate inference. The second example evaluates rotavirus vaccine introduction in Ghana and demonstrates how the analysis proceeds when the common time-varying component assumption is not supported.

The proposed conditional Poisson approach provides a practical likelihood-based framework for analyzing ITS with count outcomes using single or multiple control time series. When the common time-varying component assumption holds, incorporating multiple control series can lead to more precise estimation of the parameter of interest.